Can N be constructed?
in [Logic]
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From: George Greene on 12 Jun 2010 16:31 On Jun 12, 1:20 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > > You say the list is incomplete, therefore there must be some > > step at which you are stopping to make it so. > > Non sequitur. This is NOT a non sequitur. This is just THE TRUTH. If you never stop then you never omit any elements, so you DO cover every element and you ARE complete. > > > Which step?cannot become complete. > > None. The list is incomplete after every step. That's true, but that is only if YOU ARE STOPPING AT that step. The fact that the list was incomplete after step 2 does not make it incomplete GIVEN that we have gone PAST step 2 AND PAST ALL OTHER steps.
From: George Greene on 12 Jun 2010 16:35 WM <mueck...(a)rz.fh-augsburg.de> wrote: >The list is incomplete after every step. On Jun 12, 4:21 pm, Virgil <Vir...(a)home.esc> wrote: > But not after all steps, which makes motion possible. WM is just willfully exploiting little holes in ENGLISH at this point. "All" is AMBIGUOUS in common usage, so much so that it just ought to be outlawed in advance in this discussion. "Every" is correct; it is singular; it is about each (AND every) INDIVIDUAL. "All" is also sometimes used that way but we clearly have to have A DIFFERENT word to mean "the entire collection of" some things, considered as ONE thing. EVERY natural number is finite and is odd or even, but ALL natural numbers form an infinite collection. WM continually tries to pretend that he does not understand this distinction. Originally, I didn't know he was pretending; I thought he was just stupid. He actually continues to be stupid in belaboring these points, but in a more perverse way.
From: George Greene on 12 Jun 2010 16:40 On Jun 12, 9:15 am, WM <mueck...(a)rz.fh-augsburg.de> wrote: > Infinity never ends. These are almost as maddening as Zen koans. An infinite set may or may not have a LAST element. It may or may not have an ENDING element. The particular infinite set we are talking about here, N, does not have a last element. But it is trivial TO SIMPLY STIPULATE an ordering relation that starts with 1 as a least element and makes 0 GREATER THAN EVERY other natural number. Then, you could say, despite the fact that this set is infinite, that it, under this ordering, ENDS AT 0. w+1 is after all a valid ordinal (EVERY ordinal has a successor). More to the point, if you want (since WM said "never" and thereby invoked TIME) to STIPULATE a time for every natnum, you could just say that we "process" or "count" or check off or visit (for EVERY natnum n) n at time 1 - 2^(- n). In which case we would visit 0 at time 0, 1 at time 1/2, and FINISH visiting ALL the natnums at time 1 (AND NOT before). To say "never" is to imply that there is some small finite limit BELOW WHICH ONE CANNOT GO in processing these numbers. Since that is NOT something that WM or anybody else can ever hope to prove, I don't know what he's on about. And neither does he. Yet still we are plagued with him.
From: George Greene on 12 Jun 2010 16:45 On Jun 12, 1:20 pm, WM <mueck...(a)rz.fh-augsburg.de> wrote: > > David R Tribble wrote: > > >> If you don't stop at any finite step, how can the list be incomplete? > > > WM wrote: > > > That is the characteristic feature of an infinite list. > > > Non sequitur. The list is incomplete (only) at every finite step. > > And there is no other. But that's the whole point: whenever and wherever we are characterizing the list as complete, we ARE NOT AT ANY step! You are quite right that "there is no other": TO BE *AT* a step MEANS to HAVE STOPPED AT that step. So at THAT point, yes, YOU are incomplete. But that is a function of YOU and where YOU have stopped! It is NOT a property of the list! The list IS complete precisely BECAUSE IT INCLUDES *ALL* of these stops and steps! > > > But if you don't stop at any finite step, how can the list be > > incomplete? > > That is the property of infinity. No, that is NOT the property of infinity. Gee, that was easy. More to the point, that is not even coherent. It is just meaningless to say about an ABSTRACT object, ALL of whose parts are complete and known, that IT is incomplete. If it were actually incomplete then your description of it would ALSO be incomplete, as a result of which it would NOT be COMPLETELY determined JUST WHICH OBJECT you were even talking about.
From: Virgil on 12 Jun 2010 16:48
In article <29d2a466-c194-4cab-b842-e381b119e3fa(a)y4g2000yqy.googlegroups.com>, David R Tribble <david(a)tribble.com> wrote: > WM wrote: > >> It is not necessary to stop somewhere in order to remain in the finite > >> domain. > > > > David R Tribble wrote: > >> If you don't stop at any finite step, how can the list be incomplete? > > > > WM wrote: > > That is the characteristic feature of an infinite list. > > Non sequitur. The list is incomplete (only) at every finite step. > But if you don't stop at any finite step, how can the list be > incomplete? > > You say the list is incomplete, therefore there must be some > step at which you are stopping to make it so. Which step? WM is only able to see a sequence from within it somewhere, from which point of view only a small part of it is viewable at any one viewing. Those less handicapped are able to see a sequence from the outside, from which point of view the whole of it may be seen at once. |